Finite Group Databasebeta

← #14723746

Subgroups — #14723746

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078661C211yesmaximal, characteristic
2#13077594C211yesmaximal, characteristic, complemented
3C8×D4×D11C211yesmaximal, characteristic, complemented
4#13067478C211yesmaximal, characteristic, complemented
5#13067475C211yesmaximal, characteristic, complemented
6#13067473C211yesmaximal, characteristic, complemented
7#13067419C211yesmaximal, characteristic, complemented
8#13067415C211yesmaximal, characteristic, complemented
9D8×C11⋊C8C211yesmaximal, characteristic, complemented
10#13067408C211yesmaximal, characteristic, complemented
11#13067398C211yesmaximal, characteristic, complemented
12#13067057C211yesmaximal, characteristic, complemented
13#13067026C211yesmaximal, characteristic, complemented
14#13066895C211yesmaximal, characteristic, complemented
15C11×#1586C211yesmaximal, characteristic, complemented
16C22×C8×D11—21no—
17#10623088C2211yescharacteristic
18C4×D4×D11C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C11×#436C2211yescharacteristic, complemented
21C8×D4×C11C2211yescharacteristic
22#10622769C411yescharacteristic
23#10622766C411yescharacteristic
24#10622740—21no—
25#10622735—21no—
26C8×C22⋊D11—21no—
27C4×#4324C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29D4×C11⋊C8C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic, complemented
31#10622504C411yescharacteristic
32#10622497C411yescharacteristic
33#10622448C2211yescharacteristic
34#10622447C2211yescharacteristic
35D11×C4⋊C8C2211yescharacteristic
36#10622443C2211yescharacteristic, complemented
37#10622400C411yescharacteristic
38#10622390C411yescharacteristic
39#10622389C411yescharacteristic
40#10622376C411yescharacteristic
41(C22⋊D11)⋊C8—21no—
42(C22⋊D11)⋊C8—21no—
43D11×C22⋊C8—21no—
44#10622333—21no—
45C4×#4314C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50#10622292C2211yescharacteristic, complemented
51C11×#334C2211yescharacteristic, complemented
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic, complemented
54C11×#322C2211yescharacteristic, complemented
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic, complemented
57#10622122C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic, complemented
60#10622117C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic, complemented
63#10622094C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65C8×C11⋊C8C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×D8C2×C411yescharacteristic
70C2×C11×M16—21no—
71C22×C8×C11—21no—
72C4×D4×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74#66991C2×C411yescharacteristic
75#66989C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C4×C22⋊D11—21no—
80C4×C22⋊D11—21no—
81#66979—21no—
82C22×C11⋊C8—21no—
83C22×C11⋊C8—21no—
84C2×#4314C2×C411yescharacteristic
85C2×#4313—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89C2×C8×D11—44no—
90C2×C8×D11D411yescharacteristic
91C2×C8×D11D411yescharacteristic
92#66950C2×C411yescharacteristic
93#66946C2×C411yescharacteristic
94C4⋊C4×D11C2×C411yescharacteristic
95#66943C2×C411yescharacteristic
96#66936—21no—
97(C22⋊D11)⋊C4—21no—
98C22⋊C4×D11—21no—
99#66932—21no—
100C4×D44C2311yescharacteristic
101C42×D11C2311yescharacteristic
102C4×Dic22C2311yescharacteristic
103C11×#107C2×C411yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#102C2×C411yescharacteristic
107C11×#102C2×C411yescharacteristic
108C11×C22⋊C8—21no—
109C11×C22⋊C8—21no—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66896C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117#66885C2×C411yescharacteristic
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8C2×C411yescharacteristic
122(C2×D11)⋊C8C2×C411yescharacteristic
123#66881C2×C411yescharacteristic
124#66880C2×C411yescharacteristic
125#66879—21no—
126#66879—21no—
127#66879—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8C2×C411yescharacteristic
132Dic11⋊C8C2×C411yescharacteristic
133C8×Dic11—21no—
134C8×Dic11D411yescharacteristic
135C8×Dic11D411yescharacteristic
136#66874C2×C411yescharacteristic
137#66873C2×C411yescharacteristic
138#66872C2×C411yescharacteristic
139#66871C2×C411yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17910—111nomaximal, Sylow
146C23×D11—21no—
147C2×D4×C11C22×C411yescharacteristic
148C2×D4×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C22×Dic11—21no—
154D4×D11—22no—
155D4×D11—22no—
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11C22×C411yescharacteristic
163C2×C4×D11C2×D411yescharacteristic
164C2×C4×D11#4111yescharacteristic
165C2×Dic22C22×C411yescharacteristic
166C11×D8—22no—
167C11×M16—42no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—42no—
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C42×C11C2411yescharacteristic
181C22⋊Dic11—21no—
182C22⋊Dic11—21no—
183C22⋊Dic11—21no—
184C22⋊Dic11—21no—
185#4324—22no—
186#4323—22no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198C4×Dic11C22×C411yescharacteristic
199C4×Dic11C2×D411yescharacteristic
200C4×Dic11#4111yescharacteristic
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—42no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#4314—22no—
211#4313—24no—
212C8×D11—22no—
213C8×D11—41no—
214C8×D11—42no—
215C8×D11—42no—
216C8×D11—42no—
217#3105—111no—
218#2966—111no—
219C2×C8×D4—111no—
220#1586—111no—
221#1586D1111yescharacteristic, complemented
222#1585—111no—
223#1585—111no—
224C8×SD16—111no—
225C8×SD16—111no—
226C8×D8—111no—
227C8×D8—111no—
228#1573—111no—
229#1490—111no—
230#1483—111no—
231C8×M16—111no—
232C23×C11—21no—
233C23×C11—21no—
234C22×D11—24no—
235C22×D11—21no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11C4×D411yescharacteristic
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11#13112yes—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C22⋊D11—24no—
253C22⋊D11—42no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—42no—
258C2×Dic11C4×D411yescharacteristic
259C2×Dic11C4×D411yescharacteristic
260C2×Dic11C4×D411yescharacteristic
261D44—21no—
262D44#13112yes—
263C4×D11—22no—
264C4×D11—21no—
265C4×D11—21no—
266C4×D11—21no—
267C4×D11—21no—
268C4×D11—42no—
269C4×D11—42no—
270C4×D11—41no—
271C4×D11—41no—
272Dic22—21no—
273Dic22—21no—
274C8×C11—22no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—41no—
280C8×C11—41no—
281C11⋊C8—22no—
282C11⋊C8—21no—
283C11⋊C8—21no—
284C11⋊C8—21no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C11⋊C8AGL(1,ℤ/8)12yes—
288C23×C8—221no—
289#529—111no—
290C2×C4×D4—111no—
291#484—111no—
292#481—111no—
293#478—111no—
294#478—111no—
295#463—111no—
296#463—111no—
297#450—111no—
298#447—111no—
299#446—111no—
300C8×Q8—111no—
301C4×SD16—111no—
302C4×SD16—111no—
303C4×D8—111no—
304C4×D8C2×D1111yescharacteristic
305#436C2×D1111yescharacteristic, complemented
306#435—221no—
307C8×D4—111no—
308C8×D4—111no—
309C8×D4—111no—
310C8×D4—111no—
311C8×D4—221no—
312C8×D4—221no—
313C8×D4—221no—
314C8×D4C2×D1111yescharacteristic
315#433—221no—
316#432—111no—
317#431—111no—
318C2×C4⋊C8—111no—
319C2×C22⋊C8—221no—
320#405—221no—
321C4×M16—111no—
322C2×C4×C8—111no—
323#335—111no—
324#335—111no—
325#334—111no—
326#334C2×D1111yescharacteristic, complemented
327Q8⋊C8—111no—
328Q8⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8C2×D1111yescharacteristic
334D4⋊C8C2×D1111yescharacteristic, complemented
335#322—111no—
336#322C2×D1111yescharacteristic, complemented
337C82—111no—
338C82—111no—
339C22×C11—22no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11C2×C4×D411yescharacteristic
346C2×D11—21no—
347C2×D11—21no—
348C2×D11—22no—
349C2×D11—48no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11#44312yes—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11C2×#13111yescharacteristic
357C4×C11C2×#13111yescharacteristic
358C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
359C4×C11#57511yescharacteristic
360Dic11—21no—
361Dic11—21no—
362Dic11—21no—
363Dic11—41no—
364Dic11—41no—
365Dic11—41no—
366C22×D4—111no—
367C23×C4—221no—
368C2×SD16—111no—
369C2×SD16—111no—
370C2×D8—111no—
371C2×D8C4×D1111yescharacteristic
372C2×M16—21no—
373C2×M16—221no—
374C22×C8—21no—
375C22×C8—111no—
376C22×C8—111no—
377C22×C8—221no—
378C22×C8—221no—
379C22×C8—221no—
380C22×C8—221no—
381C22×C8—221no—
382C22×C8—444no—
383#126—221no—
384#125—111no—
385#124—111no—
386#123—221no—
387C22⋊Q8—111no—
388#121—111no—
389C4×Q8—111no—
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—111no—
393C4×D4—221no—
394C4×D4—221no—
395C4×D4—221no—
396C4×D4C22×D1111yescharacteristic
397C4×D4C22×D1111yescharacteristic
398#117—221no—
399C2×C4⋊C4—111no—
400C2×C22⋊C4—221no—
401C2×C42—111no—
402#107—111no—
403#107C4×D1111yescharacteristic
404#106—111no—
405#106—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—111no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412C4⋊C8—221no—
413C4⋊C8C22×D1111yescharacteristic
414C4⋊C8C22×D1111yescharacteristic
415#103—111no—
416#103—111no—
417#102—111no—
418#102—111no—
419#102—111no—
420#102—111no—
421#102C4×D1111yescharacteristic
422#102C4×D1111yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—111no—
426C22⋊C8—111no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432#97—221no—
433#97—221no—
434#97—221no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—111no—
439C4×C8—111no—
440C4×C8—221no—
441C4×C8C22×D1111yescharacteristic
442C4×C8C22×D1111yescharacteristic
443C4×C8C22×D1111yescharacteristic
444C2×C11—42no—
445C2×C11—81no—
446C2×C11#292911yescharacteristic
447C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
448C2×C11C2×#44311yescharacteristic
449D11—22no—
450D11—42no—
451C24—221no—
452C2×Q8—111no—
453C2×D4—111no—
454C2×D4—221no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—221no—
458C2×D4C2×C4×D1111yescharacteristic
459C2×D4C2×C4×D1111yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—442no—
470C22×C4—442no—
471SD16—222no—
472SD16—222no—
473D8—22no—
474D8—222no—
475M16—42no—
476M16—224no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—42no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—222no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—441no—
490C2×C8—442no—
491C2×C8—442no—
492C2×C8—442no—
493C2×C8—442no—
494C2×C8—442no—
495C2×C8C2×C4×D1111yescharacteristic
496C2×C8C2×C4×D1111yescharacteristic
497C2×C8D4×D1111yescharacteristic
498C2×C8D4×D1111yescharacteristic
499C4⋊C4—111no—
500C4⋊C4—111no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4C2×C4×D1111yescharacteristic
507C4⋊C4C2×C4×D1111yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C22⋊C4—221no—
515C22⋊C4—221no—
516C22⋊C4—221no—
517C42—111no—
518C42—111no—
519C42—111no—
520C42—221no—
521C42C23×D1111yescharacteristic
522C11#1791011yescharacteristic, complemented, Sylow
523C23—21no—
524C23—21no—
525C23—111no—
526C23—224no—
527C23—221no—
528C23—442no—
529C23—442no—
530Q8—221no—
531Q8—221no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—112no—
536D4—224no—
537D4—221no—
538D4—442no—
539D4#6696012yes—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—111no—
547C2×C4—111no—
548C2×C4—111no—
549C2×C4—222no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4C22×C4×D1111yescharacteristic
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C8—22no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—112no—
573C8—222no—
574C8—221no—
575C8—221no—
576C8—221no—
577C8—441no—
578C8—441no—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—112no—
586C22—221no—
587C22—221no—
588C22—222no—
589C22—448no—
590C22—441no—
591C22—441no—
592C22C4×D4×D1111yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—221no—
597C4—221no—
598C4—221no—
599C4—441no—
600C4—441no—
601C4—441no—
602C4C2×#6696011yescharacteristic
603C4D11×#13111yescharacteristic
604C4D11×AGL(1,ℤ/8)11yescharacteristic
605C4#1062330411yescharacteristic
606C2—42no—
607C2—81no—
608C2—222no—
609C2—442no—
610C2#1307730711yescharacteristic
611C2#1307742711yescharacteristic
612C2D11×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1586C2
socleC22×C11C2×C4×D4
prime radical#10622769C4
cosocleC42×C11C24
hypercenter#1586D11
hypocenterC11#17910
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13077594C2semidirect
3. C8×D4×D11C2semidirect
4. #13067478C2semidirect
5. #13067475C2semidirect
6. #13067473C2semidirect
7. #13067419C2semidirect
8. #13067415C2semidirect
9. D8×C11⋊C8C2semidirect
10. #13067408C2semidirect
11. #13067398C2semidirect
12. #13067057C2semidirect
13. #13067026C2semidirect
14. #13066895C2semidirect
15. C11×#1586C2semidirect
20. C11×#436C22semidirect
30. D4×C11⋊C8C22semidirect
36. #10622443C22semidirect
50. #10622292C22semidirect
51. C11×#334C22semidirect
53. C11×D4⋊C8C22semidirect
54. C11×#322C22semidirect
56. D4⋊(C11⋊C8)C22semidirect
57. #10622122C22semidirect
59. #10622118C22semidirect
60. #10622117C22semidirect
62. #10622096C22semidirect
63. #10622094C22semidirect
64. #10622092C22semidirect
65. C8×C11⋊C8C22semidirect
66. C8×C11⋊C8C22semidirect
221. #1586D11semidirect
305. #436C2×D11semidirect
326. #334C2×D11semidirect
334. D4⋊C8C2×D11semidirect
336. #322C2×D11semidirect
522. C11#17910semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130786612
#130775942
C8×D4×D112
#130674782
#130674752
#130674732
#130674192
#130674152
D8×C11⋊C82
#130674082
#130673982
#130670572
#130670262
#130668952
C11×#15862
#1791011